Asymptotic Expansions of acosh(x) for large x (was Unidentified s ubject!)

[Hall, Benjamin]

>I've got a problem calculating "acosh". I have to calculate cosh^(-1) of
>a very large complex number (-7.2718e+15 + 1.3382e+15i). If I try to


The wolfram website indicates some asymtotic expansions for acosh(x) for
large x

http://functions.wolfram.com/ElementaryFunctions/ArcCosh/06/01/04/

For your case it looks like 2 terms may be enough:


octave:20> z = -7.28e+15 + 1.34e+15i
z = -7.2800e+15 + 1.3400e+15i

### Asymtotic expansion for acosh(z) for large z
octave:21> y = log( -4*z^2 ) / 2 - pi*sqrt( -z^2 ) / (2*z)
y = 37.2337 +  2.9596i

octave:22> z2 = cosh(y)
z2 = -7.2800e+15 + 1.3400e+15i

octave:25> abs(z - z2)/abs(z)
ans =  1.2275e-15



-----Original Message-----
From: Serpa Gino [mailto:address@hidden
Sent: Wednesday, May 04, 2005 4:52 PM
To: address@hidden; address@hidden
Subject: RE: Unidentified subject!


How about just using 
Cosh(x)=(1/2)(e^x+e^(-x))
And solve for e^x and then for x?
Just a thought
 

-----Original Message-----
From: address@hidden [mailto:address@hidden 
Sent: Wednesday, May 04, 2005 4:42 PM
To: address@hidden
Subject: Unidentified subject!


Good afternoon,

I've got a problem calculating "acosh". I have to calculate cosh^(-1) of
a very large complex number (-7.2718e+15 + 1.3382e+15i). If I try to
calculate the value of acosh on the command line of octave, the result
is "Inf". If I've got the same in a script, the script apparently uses
this "result" for further
calculations and   I'm very suspicious about the output from this
script. Is
there a limit for the value that one can use when evaluating acosh???

Thanks,

Hana. 

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Octave is freely available under the terms of the GNU GPL.

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Octave is freely available under the terms of the GNU GPL.

Octave's home on the web:  http://www.octave.org
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Subscription information:  http://www.octave.org/archive.html
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